function [beta, gamma, alpha]=rationalHilbert(n)
H = hilb(n+1);
s = zeros(n+1, 1);
for j = 0 : n
    s(j+1) = (-1)^j;
end
t = zeros(n+1, 1);
for j = 0 : n
    for i = 1 : j
        t(j+1) = t(j+1) + (-1)^(i+j) / i;
    end
end
beta = gausslineqn(H,s,n+1);
gamma = gausslineqn(H,t,n+1);

alpha = beta * log(2) + gamma;
end